author | wenzelm |
Thu, 20 Mar 2014 21:07:57 +0100 | |
changeset 56231 | b98813774a63 |
parent 55954 | a29aefc88c8d |
child 58002 | 0ed1e999a0fb |
permissions | -rw-r--r-- |
54540 | 1 |
(* Title: HOL/Tools/coinduction.ML |
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Author: Johannes Hölzl, TU Muenchen |
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Author: Dmitriy Traytel, TU Muenchen |
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Copyright 2013 |
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Coinduction method that avoids some boilerplate compared to coinduct. |
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*) |
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signature COINDUCTION = |
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sig |
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val coinduction_tac: Proof.context -> term list -> thm option -> thm list -> cases_tactic |
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val setup: theory -> theory |
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end; |
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structure Coinduction : COINDUCTION = |
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struct |
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open Ctr_Sugar_Util |
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open Ctr_Sugar_General_Tactics |
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fun filter_in_out _ [] = ([], []) |
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| filter_in_out P (x :: xs) = (let |
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val (ins, outs) = filter_in_out P xs; |
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in |
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if P x then (x :: ins, outs) else (ins, x :: outs) |
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end); |
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fun ALLGOALS_SKIP skip tac st = |
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let fun doall n = if n = skip then all_tac else tac n THEN doall (n - 1) |
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in doall (nprems_of st) st end; |
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fun THEN_ALL_NEW_SKIP skip tac1 tac2 i st = |
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st |> (tac1 i THEN (fn st' => |
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Seq.INTERVAL tac2 (i + skip) (i + nprems_of st' - nprems_of st) st')); |
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fun DELETE_PREMS_AFTER skip tac i st = |
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let |
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val n = nth (prems_of st) (i - 1) |> Logic.strip_assums_hyp |> length; |
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in |
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(THEN_ALL_NEW_SKIP skip tac (REPEAT_DETERM_N n o etac thin_rl)) i st |
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end; |
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||
56231
b98813774a63
enforce subgoal boundaries via SUBGOAL/SUBGOAL_CASES -- clean tactical failure if out-of-range;
wenzelm
parents:
55954
diff
changeset
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fun coinduction_tac ctxt raw_vars opt_raw_thm prems = HEADGOAL (SUBGOAL_CASES (fn (goal, _, _) => |
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let |
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val lhs_of_eq = HOLogic.dest_Trueprop #> HOLogic.dest_eq #> fst; |
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fun find_coinduct t = |
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Induct.find_coinductP ctxt t @ |
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(try (Induct.find_coinductT ctxt o fastype_of o lhs_of_eq) t |> the_default []) |
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56231
b98813774a63
enforce subgoal boundaries via SUBGOAL/SUBGOAL_CASES -- clean tactical failure if out-of-range;
wenzelm
parents:
55954
diff
changeset
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val raw_thm = |
b98813774a63
enforce subgoal boundaries via SUBGOAL/SUBGOAL_CASES -- clean tactical failure if out-of-range;
wenzelm
parents:
55954
diff
changeset
|
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(case opt_raw_thm of |
b98813774a63
enforce subgoal boundaries via SUBGOAL/SUBGOAL_CASES -- clean tactical failure if out-of-range;
wenzelm
parents:
55954
diff
changeset
|
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SOME raw_thm => raw_thm |
b98813774a63
enforce subgoal boundaries via SUBGOAL/SUBGOAL_CASES -- clean tactical failure if out-of-range;
wenzelm
parents:
55954
diff
changeset
|
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| NONE => goal |> Logic.strip_assums_concl |> find_coinduct |> hd); |
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val skip = Integer.max 1 (Rule_Cases.get_consumes raw_thm) - 1 |
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val cases = Rule_Cases.get raw_thm |> fst |
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in |
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56231
b98813774a63
enforce subgoal boundaries via SUBGOAL/SUBGOAL_CASES -- clean tactical failure if out-of-range;
wenzelm
parents:
55954
diff
changeset
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HEADGOAL ( |
54742
7a86358a3c0b
proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
wenzelm
parents:
54540
diff
changeset
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Object_Logic.rulify_tac ctxt THEN' |
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Method.insert_tac prems THEN' |
54742
7a86358a3c0b
proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
wenzelm
parents:
54540
diff
changeset
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Object_Logic.atomize_prems_tac ctxt THEN' |
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DELETE_PREMS_AFTER skip (Subgoal.FOCUS (fn {concl, context = ctxt, params, prems, ...} => |
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let |
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val vars = raw_vars @ map (term_of o snd) params; |
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val names_ctxt = ctxt |
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|> fold Variable.declare_names vars |
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|> fold Variable.declare_thm (raw_thm :: prems); |
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val thm_concl = Thm.cprop_of raw_thm |> strip_imp_concl; |
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val (rhoTs, rhots) = Thm.match (thm_concl, concl) |
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|>> map (pairself typ_of) |
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||> map (pairself term_of); |
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val xs = hd (Thm.prems_of raw_thm) |> HOLogic.dest_Trueprop |> strip_comb |> snd |
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|> map (subst_atomic_types rhoTs); |
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val raw_eqs = map (fn x => (x, AList.lookup op aconv rhots x |> the)) xs; |
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val ((names, ctxt), Ts) = map_split (apfst fst o dest_Var o fst) raw_eqs |
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|>> (fn names => Variable.variant_fixes names names_ctxt) ; |
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val eqs = |
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map3 (fn name => fn T => fn (_, rhs) => |
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HOLogic.mk_eq (Free (name, T), rhs)) |
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names Ts raw_eqs; |
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54366
13bfdbcfbbfb
swap equations and premises in the coinductive step for better proof automation
Andreas Lochbihler
parents:
54026
diff
changeset
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val phi = eqs @ map (HOLogic.dest_Trueprop o prop_of) prems |
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|> try (Library.foldr1 HOLogic.mk_conj) |
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|> the_default @{term True} |
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|> list_exists_free vars |
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|> Term.map_abs_vars (Variable.revert_fixed ctxt) |
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|> fold_rev Term.absfree (names ~~ Ts) |
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|> certify ctxt; |
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val thm = cterm_instantiate_pos [SOME phi] raw_thm; |
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val e = length eqs; |
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val p = length prems; |
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in |
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HEADGOAL (EVERY' [rtac thm, |
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EVERY' (map (fn var => |
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rtac (cterm_instantiate_pos [NONE, SOME (certify ctxt var)] exI)) vars), |
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54366
13bfdbcfbbfb
swap equations and premises in the coinductive step for better proof automation
Andreas Lochbihler
parents:
54026
diff
changeset
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if p = 0 then CONJ_WRAP' (K (rtac refl)) eqs |
13bfdbcfbbfb
swap equations and premises in the coinductive step for better proof automation
Andreas Lochbihler
parents:
54026
diff
changeset
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else REPEAT_DETERM_N e o (rtac conjI THEN' rtac refl) THEN' CONJ_WRAP' rtac prems, |
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K (ALLGOALS_SKIP skip |
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(REPEAT_DETERM_N (length vars) o (etac exE THEN' rotate_tac ~1) THEN' |
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DELETE_PREMS_AFTER 0 (Subgoal.FOCUS (fn {prems, params, context = ctxt, ...} => |
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(case prems of |
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[] => all_tac |
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| inv::case_prems => |
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let |
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val (init, last) = funpow_yield (p + e - 1) HOLogic.conj_elim inv; |
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val inv_thms = init @ [last]; |
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54366
13bfdbcfbbfb
swap equations and premises in the coinductive step for better proof automation
Andreas Lochbihler
parents:
54026
diff
changeset
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val eqs = take e inv_thms; |
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fun is_local_var t = |
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member (fn (t, (_, t')) => t aconv (term_of t')) params t; |
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val (eqs, assms') = filter_in_out (is_local_var o lhs_of_eq o prop_of) eqs; |
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54366
13bfdbcfbbfb
swap equations and premises in the coinductive step for better proof automation
Andreas Lochbihler
parents:
54026
diff
changeset
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val assms = assms' @ drop e inv_thms |
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in |
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HEADGOAL (Method.insert_tac (assms @ case_prems)) THEN |
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unfold_thms_tac ctxt eqs |
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end)) ctxt)))]) |
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end) ctxt) THEN' |
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56231
b98813774a63
enforce subgoal boundaries via SUBGOAL/SUBGOAL_CASES -- clean tactical failure if out-of-range;
wenzelm
parents:
55954
diff
changeset
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K (prune_params_tac ctxt)) |
b98813774a63
enforce subgoal boundaries via SUBGOAL/SUBGOAL_CASES -- clean tactical failure if out-of-range;
wenzelm
parents:
55954
diff
changeset
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#> Seq.maps (fn st => |
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CASES (Rule_Cases.make_common (Proof_Context.theory_of ctxt, prop_of st) cases) all_tac st) |
56231
b98813774a63
enforce subgoal boundaries via SUBGOAL/SUBGOAL_CASES -- clean tactical failure if out-of-range;
wenzelm
parents:
55954
diff
changeset
|
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end)); |
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local |
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val ruleN = "rule" |
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val arbitraryN = "arbitrary" |
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fun single_rule [rule] = rule |
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| single_rule _ = error "Single rule expected"; |
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fun named_rule k arg get = |
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Scan.lift (Args.$$$ k -- Args.colon) |-- Scan.repeat arg :|-- |
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(fn names => Scan.peek (fn context => Scan.succeed (names |> map (fn name => |
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(case get (Context.proof_of context) name of SOME x => x |
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| NONE => error ("No rule for " ^ k ^ " " ^ quote name)))))); |
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fun rule get_type get_pred = |
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c07d184aebe9
tuned signature -- more uniform check_type_name/read_type_name;
wenzelm
parents:
54742
diff
changeset
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named_rule Induct.typeN (Args.type_name {proper = false, strict = false}) get_type || |
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named_rule Induct.predN (Args.const {proper = false, strict = false}) get_pred || |
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named_rule Induct.setN (Args.const {proper = false, strict = false}) get_pred || |
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Scan.lift (Args.$$$ ruleN -- Args.colon) |-- Attrib.thms; |
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val coinduct_rule = rule Induct.lookup_coinductT Induct.lookup_coinductP >> single_rule; |
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fun unless_more_args scan = Scan.unless (Scan.lift |
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((Args.$$$ arbitraryN || Args.$$$ Induct.typeN || |
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Args.$$$ Induct.predN || Args.$$$ Induct.setN || Args.$$$ ruleN) -- Args.colon)) scan; |
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val arbitrary = Scan.optional (Scan.lift (Args.$$$ arbitraryN -- Args.colon) |-- |
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Scan.repeat1 (unless_more_args Args.term)) []; |
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in |
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val setup = |
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Method.setup @{binding coinduction} |
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(arbitrary -- Scan.option coinduct_rule >> |
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(fn (arbitrary, opt_rule) => fn ctxt => |
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RAW_METHOD_CASES (fn facts => |
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Seq.DETERM (coinduction_tac ctxt arbitrary opt_rule facts)))) |
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"coinduction on types or predicates/sets"; |
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end; |
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end; |
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